adding components to a gameObject in a list of lists

im trying to add components to a gameobject thats inside a list of lists,

im getting the error

Assets/createplane.cs(151,71): error CS1061: Type System.Collections.Generic.List' does not contain a definition for AddComponent' and no extension method AddComponent' of type System.Collections.Generic.List' could be found (are you missing a using directive or an assembly reference?)

the error is on the line

MeshFilter meshFilter = (MeshFilter)thePlanes[(int)z].AddComponent(typeof(MeshFilter));

i think im not accessing the .addcomponent of the gameobject in the list properly, but im not sure,

 List<List<GameObject>> thePlanes;
 
 void Awake()
     {
         List<List<GameObject>> thePlanes = new List<List<GameObject>>();
         
         for(float i = 0;i<planecount;i++)
         {
             thePlanes.Add(new List<GameObject>());
             
             for(float j = 0;j<planecount;j++)    
             {
                 MakePlane(i,j);
             }
         }
     }
 
 void MakePlane(float x, float z)
     {
         //GameObject plane = new GameObject("Plane x="+x+" z="+z);
         thePlanes[(int)z].Add(new GameObject("Plane x="+x+" z="+z));
         //MeshFilter meshFilter = (MeshFilter)plane.AddComponent(typeof(MeshFilter));
         MeshFilter meshFilter = (MeshFilter)thePlanes[(int)z].AddComponent(typeof(MeshFilter));
         meshFilter.mesh = CreatePlane(size);
         //MeshRenderer renderer = plane.AddComponent(typeof(MeshRenderer)) as MeshRenderer;
         MeshRenderer renderer = (MeshRenderer)thePlanes[(int)z].AddComponent(typeof(MeshRenderer));
             renderer.material.shader = Shader.Find ("Particles/Additive");
         Texture2D tex = new Texture2D(1, 1);
         tex.SetPixel(0, 0, Color.green);
         tex.Apply();
         renderer.material.mainTexture = tex;
            renderer.material.color = Color.green;
         meshFilter.transform.Translate(new Vector3((x*size*(size-1)),0,(z*size*(size-1))));
         //thePlanes[(int)z].Add(plane);
     }

i think ive got it correct, im doing it the same way i was doing it before i put them in the list, but its not working for this